Crack Paths 2012

shown in Fig. 2. The expected time to crack growth from the initial detected length a0 to

the critical length ac is expressed by:

⎡

⎤

(h1) 132n−7() h 2 ) 23 2 + 19 (h3) 132n−7() h

(h

⎞

⎛

32n−7() ) 23 2

(

)1−n

aa0c ∫

da

⎛

−1

⎞

πa

Ta0,ac()=2πλ2/λ4Cσ Xn−1

Y

Kc

(h1) 1

⎢

⎥

⎟

⎜

⎝ ⎜

⎠ ⎟

⎢

⎥

4 ) 23n−2()

−

⎠ ⎟

πa

⎝ ⎜

3σXY

⎣ ⎢

⎦ ⎥

2

hi = hiαX,βX()

λ02λ4 βX =

λλ01λ2 σX =

λ

αX =

0

+ ∞

ω iS

= 2

ω( )dω

λ

∫

i

X

(2)

0

where C, n, Kc are materials constant involved in the Forman crack propagation law and

determined through non-linear fitting of the Paris curve plotted in Fig. 5, σX is the

standard deviation of the random stress process, hi (i=1,…,4) are stochastic mean

functions of the irregularity factor αX and wide band parameter βX, which in turn

depend on the i-order spectral momentof the random stress process, and Y is the crack

shape-factor computed in [5].

Figure 10. Time to structural collapse as a function of the initial detected crack length.

It has been assumed that the wind direction is approximately constant during the

integration interval. This is consistent with anemometric investigations of the site where

the turbine is installed which attest preferential N N W - S SwEind direction and diurnal

excursions in the blowing orientation. Since the fluctuating (zero-mean) wind actions

are preponderant with respect with the static alongwind loading, the change in wind

orientation is expected not to significantly affect the estimations made using Eq. (2).

Obviously, this model does not take into account the occurrence of wind gusts during

wind turbine operation. However, the present approach is deemed conservative because

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